Error analysis, measurement and compensation method for high-precision air floatation linear motion platform

Abstract

The invention discloses a high-precision air floatation linear motion platform error analysis, measurement and compensation method, which relates to the technical field of linear motion error analysis, and comprises the following steps: constructing a global geometric error model considering translation and rotation angle error coupling on the basis of a gantry structure of a platform, constructing a laser interferometer measurement system, and calculating the linear motion error. Six geometric errors of the air floating platform are accurately measured, and submicron and sub-arc second magnitude original data are obtained. And performing polynomial fitting on the error data by using a least square method, establishing a function expression of a relative displacement instruction, introducing an error function into a servo control system, and constructing a real-time error compensation method based on position loop feedforward. The air floating platform experiment shows that the modeling method can accurately describe the geometric error of the platform motion, the measurement system can obtain high-precision data, the compensation method obviously improves the positioning precision, various error indexes are obviously improved, and a foundation is built for the air floating platform to realize nanoscale ultra-precision motion control.

Description

Technical Field

[0001] The invention relates to the technical field of linear motion error analysis, and in particular to a method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform. Background Art

[0002] With the rapid development of semiconductor manufacturing, precision optics, biomedicine and other fields, higher and higher requirements are placed on the positioning accuracy of ultra-precision motion platforms. Air-floating linear motion platforms have been widely used in nano-scale processing and detection equipment due to their advantages such as low friction, high rigidity and no wear. However, air-floating platforms will inevitably introduce geometric errors during the manufacturing and assembly process, causing the actual motion trajectory of the workbench to deviate from the ideal straight line, seriously affecting the positioning accuracy of the platform. Therefore, research on geometric error modeling, measurement and compensation of air-floating platforms is of great significance to improving the level of ultra-precision processing and detection.

[0003] The existing high-precision air-floating linear motion platform error analysis, measurement, and compensation methods mainly focus on the measurement method of single error, lack the analysis of the global error characteristics of the air-floating platform, and have low measurement efficiency, which restricts its application in ultra-precision motion control. Therefore, it is necessary to provide a high-precision air-floating linear motion platform error analysis, measurement, and compensation method to solve the above-mentioned problems. Summary of the invention

[0004] In order to solve the above technical problems, a high-precision air-floating linear motion platform error analysis, measurement and compensation method is provided. This technical solution solves the problem that the existing high-precision air-floating linear motion platform error analysis, measurement and compensation method proposed in the above background technology mainly focuses on the measurement method of a single error and lacks analysis of the global error characteristics of the air-floating platform.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A high-precision air-floating linear motion platform error analysis, measurement, and compensation method, comprising:

[0007] S100, obtaining gantry structure information of the air floating platform, and constructing a fixed coordinate system B, a moving coordinate system X, a moving coordinate system Y and a moving coordinate system T based on the gantry structure information;

[0008] S200, constructing a homogeneous transformation matrix through the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, and obtaining the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T;

[0009] S300, obtaining a complete geometric error model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B according to the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T;

[0010] S400, setting a target point, and obtaining actual position information of the target point according to a complete model of geometric errors;

[0011] S500, based on the gantry structure information of the air-floating platform, build a high-precision measurement system, and obtain the geometric error data of the air-floating platform during its movement through the high-precision measurement system;

[0012] S600, performing parameter identification on the geometric error data based on the least square method to obtain a functional relationship between the geometric error and the displacement instruction;

[0013] S700, according to the functional relationship between the geometric error and the displacement command, the actual position information is corrected to obtain the compensated standard position information, and the closed-loop geometric error compensation is completed.

[0014] In an optional embodiment, the step of obtaining the gantry structure information of the air floating platform and constructing a fixed coordinate system B, a moving coordinate system X, a moving coordinate system Y and a moving coordinate system T based on the gantry structure information specifically includes:

[0015] Based on the gantry structure information of the air floating platform, the marble base structure information, the X-axis drive module structure information, the Y-axis drive module structure information and the workbench structure information are obtained;

[0016] According to the X-axis driving module structure information, the X-axis hydrostatic guide rail structure information and the X-axis motor driving slider structure information are obtained;

[0017] According to the Y-axis driving module structure information, the Y-axis hydrostatic guide structure information and the Y-axis motor driving slider structure information are obtained;

[0018] Based on the structure information of the marble base, a fixed coordinate system B is established, wherein the X axis and the Y axis of the fixed coordinate system are parallel to the length direction and the width direction of the marble base respectively;

[0019] Based on the structural information of the slider driven by the X-axis motor, a moving coordinate system X is constructed, and based on the structural information of the slider driven by the Y-axis motor, a moving coordinate system Y is constructed, wherein the moving coordinate system X and the moving coordinate system Y move along the X-axis and the Y-axis of the fixed coordinate system B respectively;

[0020] Based on the workbench structure information, a moving coordinate system T is constructed, and the origin of the coordinate system T is located at the intersection of the moving coordinate system X and the moving coordinate system Y.

[0021] In an optional embodiment, the homogeneous transformation matrix is ​​constructed by using the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, and the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T are obtained, specifically including:

[0022] Based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the worktable is controlled to move along the X-axis and Y-axis directions of the fixed coordinate system B, and the motion information of the moving coordinate system X and the moving coordinate system Y is obtained;

[0023] When the workbench moves along the X-axis and Y-axis directions of the fixed coordinate system B, the position information and posture change information of the origin coordinates of the moving coordinate system T relative to the fixed coordinate system B are obtained;

[0024] According to the motion information of the moving coordinate system X and the moving coordinate system Y, as well as the position information and attitude change information of the origin coordinate of the moving coordinate system T relative to the fixed coordinate system B, the homogeneous transformation matrix of formula (1) can be obtained:

[0025]

[0026] in, is the rotation transformation matrix of the origin coordinates of the moving coordinate system T relative to the fixed coordinate system B, is the position vector of the origin of the moving coordinate system T in the fixed coordinate system B, δ x ,δ y ,δ z are straightness errors, which represent the displacement deviations of the origin coordinates of the moving coordinate system T in the X, Y and Z directions respectively. α, β and γ are all angular errors, which represent the rotational deviations of the origin coordinates of the moving coordinate system T around the X, Y and Z axes respectively.

[0027] In an optional embodiment, the geometric error complete model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B is obtained based on the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T, specifically including:

[0028] Since the magnitude of the translation error and the rotation error is very small, R B T Do Taylor expansion near the zero point and take the first-order approximation, then we have:

[0029]

[0030] Will and Substituting them into equation (1) respectively and ignoring small quantities above the second order, we can get:

[0031]

[0032] Formula (3) is the complete geometric error model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B.

[0033] In an optional embodiment, the step of setting a target point and obtaining actual position information of the target point according to a complete geometric error model specifically includes:

[0034] Assume that a target point on the workbench is P, then the position vector of P in the moving coordinate system T is Then the actual position of P in the fixed coordinate system B is:

[0035]

[0036] Formula (4) shows that the actual position of the target point P in B is not only affected by the position error of the origin T (δ x ,δ y ,δ z ), and is also affected by the coupling of the angular errors (α, β, γ).

[0037] In an optional embodiment, the high-precision measurement system is built based on the gantry structure information of the air-floating platform, and the geometric error data of the air-floating platform during movement is obtained through the high-precision measurement system, specifically including:

[0038] Based on the gantry structure information of the air floating platform, the marble base structure information, the X-axis drive module structure information, the Y-axis drive module structure information and the workbench structure information are obtained;

[0039] Based on the structure information of the marble base, determine the installation position information of the corner cube prism;

[0040] Determine the laser head installation position information based on the X-direction drive module structure information and the Y-direction drive module structure information;

[0041] Based on the workbench structure information, determine the interferometer installation position information;

[0042] According to the installation position information of the corner cube prism, the installation position information of the laser head and the installation position information of the interferometer, the corner cube prism, the laser head and the interferometer are installed to build a high-precision measurement system;

[0043] Adjust the laser head so that the incident laser light is collinear with the X-axis of the fixed coordinate system B;

[0044] Based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the worktable is controlled to make a fixed distance incremental movement Δx along the X-axis movement direction of the fixed coordinate system B, and the corresponding fringe count change ΔN is recorded at the same time;

[0045] According to the fixed distance incremental movement Δx and the fringe count change ΔN, the straightness error at the kth displacement point is obtained:

[0046]

[0047] In formula (5), λ is the laser wavelength, and the straightness error δ at all displacement points is z (x k ) is used for least squares fitting, and the continuous function expression of the X-axis vertical error δ can be obtained. z (x);

[0048] Similarly, the X-axis horizontal straightness error δ can be obtained y (x), Y axis horizontal straightness error δ x (y) and Y axis vertical straightness error δ z (y);

[0049] Combining the X-axis vertical error, X-axis horizontal straightness error, Y-axis horizontal straightness error and Y-axis vertical straightness error, the four straightness errors are orthogonal to each other to form the translation error vector of the air floating platform.

[0050] In an optional embodiment, the high-precision measurement system is built based on the gantry structure information of the air-floating platform, and the geometric error data of the air-floating platform during movement is obtained through the high-precision measurement system, specifically including:

[0051] Based on the interferometer installation position information, an angle interferometer is installed, and based on the workbench structure information and the corner cube installation position information, a corner cube is installed on the workbench;

[0052] Adjust the angle interferometer so that its measuring light is parallel to the X-axis of the fixed coordinate system B and the reference light is perpendicular to the X-axis;

[0053] Based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the workbench is controlled to make a fixed distance incremental movement Δx again, and the corresponding angle fringe change ΔN is recorded. α , then the pitch angle error at the kth displacement point is:

[0054]

[0055] Where d is the effective aperture of the corner cube prism, for discrete data points α(x k ) performs least square fitting to obtain the continuous function α(x);

[0056] Similarly, the X-axis yaw angle error β(x), the Y-axis yaw angle error γ(y), and the Y-axis pitch angle error β(y) can be measured;

[0057] Combining the X-axis pitch angle error, the X-axis yaw angle error, the Y-axis yaw angle error and the Y-axis pitch angle error, the angular error vector of the air floating platform is formed;

[0058] The translation error vector and rotation error vector of the air-floating platform are integrated to obtain the geometric error data during the movement of the air-floating platform.

[0059] In an optional embodiment, the method of performing parameter identification on the geometric error data based on the least square method to obtain a functional relationship between the geometric error and the displacement instruction specifically includes:

[0060] Through the high-precision measurement system, the four translation error components and four rotation error components of the air-floating platform in the X and Y directions were measured one by one. The continuous function expressions of the relative displacement of the eight geometric errors were obtained by least squares fitting.

[0061] Through equations (1) and (3), the geometric error of the air-floating platform is determined as a function of the displacement command;

[0062] The function expression of geometric error relative displacement is obtained from discrete data using the least squares method:

[0063] Get the vertical linear error δ in the X-axis direction z (x), the vertical straight line error δ z (x) is converted to an n-order polynomial:

[0064] δ z (x) = a0 + a1x + a2x 2 +…+a n x n

[0066] (7) where a0,…,a n As the parameters to be identified, the m groups of data points (x i ,δ zi Substituting )(i=1,2,…,m) into equation (9), we get the error equation:

[0067]

[0068] Where v i is the residual of the ith data point, let x = [x1, x2, …, x m ] T , δ z =[δ z1 ,δ z2 ,…,δ zm ] T ,a=[a0,a1,…,a n ] T , convert formula (8) into matrix form:

[0069] v=Xa-δ z (9)

[0070] Where X is the coefficient matrix:

[0071]

[0072] Based on the least squares criterion, let the error sum of squares v T When v takes a minimum value, the estimated value of a is:

[0073]

[0074] Will Substituting into formula (9), we get the vertical straightness error δ z The least squares polynomial fit of (x);

[0075] Similarly, the function expressions of the relative displacement instructions corresponding to the X-axis vertical error, X-axis horizontal straightness error, Y-axis horizontal straightness error, Y-axis vertical straightness error, X-axis pitch angle error, X-axis yaw angle error, Y-axis yaw angle error and Y-axis pitch angle error can be obtained.

[0076] In an optional embodiment, the actual position information is corrected according to the functional relationship between the geometric error and the displacement instruction to obtain the compensated standard position information to complete the closed-loop geometric error compensation, which specifically includes:

[0077] Obtaining the structural information of the servo control system of the air floating platform, and determining the position loop information, speed loop information and current loop information, and obtaining the position command information output by the servo control system;

[0078] Based on the position loop information, a feedforward compensation link is introduced, and the functional relationship between the geometric error and the displacement command is used to correct the x in the position command information. c ,y c Make corrections to obtain the compensated position command Assume that the position command output by the servo control system at the kth sampling moment is (x c (k), y c (k)), and substituting it into the geometric error model of formula (3), we can get:

[0079]

[0080] Among them, the position instruction (x c (k),y c (k)) corresponds to three translation errors and three rotation errors.

[0081] In an optional embodiment, the actual position information is corrected according to the functional relationship between the geometric error and the displacement instruction to obtain the compensated standard position information to complete the closed-loop geometric error compensation, which specifically includes:

[0082] According to formula (4), the position compensation of the worktable target point P in the fixed coordinate system B is:

[0083]

[0084] The compensation in formula (13) includes the translation error and the angular error, as well as the coupling effect between the two. The compensation is added to the position command output by the servo control system to obtain the corrected command:

[0085]

[0086] Based on the speed loop information and the current loop information, the corrected command is input into the speed loop and the current loop, so that the servo control system drives the air floating platform to move and obtains the compensated standard position information.

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] This scheme proposes a method for error analysis, measurement, and compensation of a high-precision air-floating linear motion platform. By comprehensively considering the coupling characteristics of translation error and angular error, an accurate global geometric error model is established, and a laser interferometer is used to achieve high-precision error measurement at the sub-micron and sub-arcsecond levels. The least squares method is used to perform function fitting on the error data to quickly obtain the functional relationship between the geometric error and the displacement command, providing an accurate mathematical model for real-time compensation. The error function is introduced into the servo control system to achieve real-time error compensation, so that the actual motion trajectory of the platform is greatly close to the ideal straight line, significantly improving the positioning accuracy of the platform. It is suitable for high-precision air-floating linear motion platforms of various gantry structures, has good versatility and scalability, and can meet the needs of ultra-precision motion control in different fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 A flowchart of the error analysis, measurement and compensation method of a high-precision air-floating linear motion platform proposed by the present invention;

[0090] Figure 2 A specific flow chart for constructing the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T in the present invention;

[0091] Figure 3 and Figure 4 The combination is a flow chart for obtaining geometric error data in the present invention. DETAILED DESCRIPTION

[0092] The following description is used to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are only examples, and those skilled in the art may think of other obvious variations.

[0093] Reference Figure 1 - Figure 4 As shown, a method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform includes:

[0094] S100, obtaining gantry structure information of the air floating platform, and constructing a fixed coordinate system B, a moving coordinate system X, a moving coordinate system Y and a moving coordinate system T based on the gantry structure information;

[0095] S200, constructing a homogeneous transformation matrix through the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, and obtaining the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T;

[0096] S300, obtaining a complete geometric error model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B according to the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T;

[0097] S400, setting a target point, and obtaining actual position information of the target point according to a complete model of geometric errors;

[0098] S500, based on the gantry structure information of the air-floating platform, build a high-precision measurement system, and obtain the geometric error data of the air-floating platform during its movement through the high-precision measurement system;

[0099] S600, performing parameter identification on the geometric error data based on the least square method to obtain a functional relationship between the geometric error and the displacement instruction;

[0100] S700, according to the functional relationship between the geometric error and the displacement command, the actual position information is corrected to obtain the compensated standard position information, and the closed-loop geometric error compensation is completed.

[0101] Furthermore, the gantry structure information of the air floating platform is obtained, and the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T are constructed based on the gantry structure information, specifically including:

[0102] Based on the gantry structure information of the air floating platform, the marble base structure information, the X-axis drive module structure information, the Y-axis drive module structure information and the workbench structure information are obtained;

[0103] According to the X-axis driving module structure information, the X-axis hydrostatic guide rail structure information and the X-axis motor driving slider structure information are obtained;

[0104] According to the Y-axis driving module structure information, the Y-axis hydrostatic guide structure information and the Y-axis motor driving slider structure information are obtained;

[0105] Based on the structural information of the marble base, a fixed coordinate system B is established, and the X-axis and Y-axis of the fixed coordinate system are parallel to the length direction and width direction of the marble base respectively;

[0106] Based on the structural information of the slider driven by the X-axis motor, a moving coordinate system X is constructed, and based on the structural information of the slider driven by the Y-axis motor, a moving coordinate system Y is constructed. The moving coordinate system X and the moving coordinate system Y move along the X-axis and Y-axis of the fixed coordinate system B respectively.

[0107] Based on the workbench structure information, a moving coordinate system T is constructed, and the origin of the coordinate system T is located at the intersection of the moving coordinate system X and the moving coordinate system Y.

[0108] Furthermore, a homogeneous transformation matrix is ​​constructed through the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, and the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T are obtained, specifically including:

[0109] Based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the worktable is controlled to move along the X-axis and Y-axis directions of the fixed coordinate system B, and the motion information of the moving coordinate system X and the moving coordinate system Y is obtained;

[0110] When the workbench moves along the X-axis and Y-axis directions of the fixed coordinate system B, the position information and posture change information of the origin coordinates of the moving coordinate system T relative to the fixed coordinate system B are obtained;

[0111] According to the motion information of the moving coordinate system X and the moving coordinate system Y, as well as the position information and attitude change information of the origin coordinate of the moving coordinate system T relative to the fixed coordinate system B, the homogeneous transformation matrix of formula (1) can be obtained:

[0112]

[0113] in, is the rotation transformation matrix of the origin coordinates of the moving coordinate system T relative to the fixed coordinate system B, is the position vector of the origin of the moving coordinate system T in the fixed coordinate system B, δ x ,δ y ,δ z is the straightness error, which respectively represents the displacement deviation of the origin coordinate of the moving coordinate system T in the X, Y and Z directions. α, β and γ are all angle errors, which respectively represent the rotation angle deviation of the origin coordinate of the moving coordinate system T around the X, Y and Z axes. Formula (1) reflects the geometric error characteristics during the platform motion process.

[0114] Furthermore, based on the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T, a complete geometric error model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B is obtained, which specifically includes:

[0115] Since the magnitude of the translation error and the rotation error is very small, Do Taylor expansion near the zero point and take the first-order approximation, then we have:

[0116]

[0117] Will and Substituting them into equation (1) respectively and ignoring small quantities above the second order, we can get:

[0118]

[0119] Formula (3) is the complete geometric error model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B, which reflects the coupling characteristics of the translation error and the angular deviation. x ,δ y ,δ z It is not only related to the displacement in its own direction of motion, but also affected by the displacement in another direction. It is a binary function. The angular deviations α, β, and γ also show similar coupling characteristics.

[0120] Furthermore, the target point is set, and the actual position information of the target point is obtained according to the complete model of geometric error, including:

[0121] Assume that a target point on the workbench is P, then the position vector of P in the moving coordinate system T is Then the actual position of P in the fixed coordinate system B is:

[0122]

[0123] Formula (4) shows that the actual position of the target point P in B is not only affected by the position error of the origin T (δ x ,δ y ,δ z ), and is also affected by the coupling of the angular error (α, β, γ), where the angular error is coupled through the coupling term Affecting the position of the target point, these coupling errors will cause the actual trajectory of the target point to deviate from the ideal straight line.

[0124] Specifically, the steps S100-S400 fully consider the coupling characteristics of translation error and angular error in dual-axis motion, and can accurately reflect the law of platform motion error. On this basis, by precisely measuring and identifying the functions of the six geometric error components and introducing real-time compensation links, the positioning accuracy of the platform can be effectively improved.

[0125] Furthermore, based on the gantry structure information of the air-floating platform, a high-precision measurement system is built, and the geometric error data of the air-floating platform during movement is obtained through the high-precision measurement system, including:

[0126] Based on the gantry structure information of the air floating platform, the marble base structure information, the X-axis drive module structure information, the Y-axis drive module structure information and the workbench structure information are obtained;

[0127] Based on the structure information of the marble base, determine the installation position information of the corner cube prism;

[0128] Determine the laser head installation position information based on the X-direction drive module structure information and the Y-direction drive module structure information;

[0129] Based on the workbench structure information, determine the interferometer installation position information;

[0130] According to the installation position information of the corner cube prism, the installation position information of the laser head and the installation position information of the interferometer, the corner cube prism, the laser head and the interferometer are installed to build a high-precision measurement system;

[0131] Adjust the laser head so that the incident laser light is collinear with the X-axis of the fixed coordinate system B;

[0132] Based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the worktable is controlled to make a fixed distance incremental movement Δx along the X-axis movement direction of the fixed coordinate system B, and the corresponding fringe count change ΔN is recorded at the same time;

[0133] According to the fixed distance incremental movement Δx and the fringe count change ΔN, the straightness error at the kth displacement point is obtained:

[0134]

[0135] In formula (5), λ is the laser wavelength, and the straightness error δ at all displacement points is z (x k ) is used for least squares fitting, and the continuous function expression of the X-axis vertical error δ can be obtained. z (x);

[0136] Similarly, the X-axis horizontal straightness error δ can be obtained y (x), Y axis horizontal straightness error δ x (y) and Y axis vertical straightness error δ z (y);

[0137] Combining the X-axis vertical error, X-axis horizontal straightness error, Y-axis horizontal straightness error and Y-axis vertical straightness error, the four straightness errors are orthogonal to each other to form the translation error vector of the air floating platform.

[0138] Furthermore, based on the gantry structure information of the air-floating platform, a high-precision measurement system is built, and the geometric error data of the air-floating platform during movement is obtained through the high-precision measurement system, including:

[0139] Based on the interferometer installation position information, an angle interferometer is installed, and based on the workbench structure information and the corner cube installation position information, a corner cube is installed on the workbench;

[0140] Adjust the angle interferometer so that its measuring light is parallel to the X-axis of the fixed coordinate system B and the reference light is perpendicular to the X-axis;

[0141] Based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the workbench is controlled to make a fixed distance incremental movement Δx again, and the corresponding angle fringe change ΔN is recorded. α , then the pitch angle error at the kth displacement point is:

[0142]

[0143] Where d is the effective aperture of the corner cube prism, for discrete data points α(x k ) performs least square fitting to obtain the continuous function α(x);

[0144] Similarly, the X-axis yaw angle error β(x), the Y-axis yaw angle error γ(y), and the Y-axis pitch angle error β(y) can be measured;

[0145] Combining the X-axis pitch angle error, the X-axis yaw angle error, the Y-axis yaw angle error and the Y-axis pitch angle error, the angular error vector of the air floating platform is formed;

[0146] The translation error vector and rotation error vector of the air-floating platform are integrated to obtain the geometric error data during the movement of the air-floating platform.

[0147] Specifically, in order to obtain the geometric error data of the air-floating platform, the high-precision measurement system in this scheme is built through a laser interferometer. The Renishaw XL-80 laser interferometer is used, which adopts the dynamic dual-frequency method to achieve nanometer-level displacement detection by measuring the interference phase difference between the laser reference light and the measurement light. The XL-80 is mainly composed of a laser head, an interferometer, a compensation device, etc. Among them, the frequency stability of the He-Ne laser output by the laser head reaches 0.05ppm, and the measurement linearity is better than 0.5ppm. The interferometer divides the incident laser into two beams of the same frequency, one beam is used as a reference light to irradiate the reference mirror, and the other beam is used as a measurement light to irradiate the workbench reflector. The two beams of light interfere at the detector to generate a fringe signal proportional to the displacement. The displacement measurement value can be obtained by demodulation. Environmental sensors measure parameters such as temperature, air pressure, and humidity for atmospheric refractive index compensation. The measurement repeatability of the entire system is better than 1nm, which is very suitable for precision error detection.

[0148] Furthermore, the geometric error data is parameter identified based on the least square method to obtain the functional relationship between the geometric error and the displacement instruction, which specifically includes:

[0149] Through the high-precision measurement system, the four translation error components and four rotation error components of the air-floating platform in the X and Y directions were measured one by one. The continuous function expressions of the relative displacement of the eight geometric errors were obtained by least squares fitting.

[0150] Through equations (1) and (3), the geometric error of the air-floating platform is determined as a function of the displacement command;

[0151] The function expression of geometric error relative displacement is obtained from discrete data using the least squares method:

[0152] Get the vertical linear error δ in the X-axis direction z (x), the vertical straight line error δ z (x) is converted to an n-order polynomial:

[0153] δ z (x) = a0 + a1x + a2x 2 +…+a n x n

[0155] (7) where a0, δ, a n As the parameters to be identified, the m groups of data points (x i ,δ zi Substituting )(i=1,2,δ,m) into equation (9), we get the error equation:

[0156]

[0157] Where v i is the residual of the ith data point, let x = [x1, x2, …, x m ] T , δ z =[δ z1 ,δ z2 ,…,δ zm ] T ,a=[a0,a1,…,a n ] T , convert formula (8) into matrix form:

[0158] v=Xa-δ z (9)

[0159] Where X is the coefficient matrix:

[0160]

[0161] Based on the least squares criterion, let the error sum of squares v T When v takes a minimum value, the estimated value of a is:

[0162]

[0163] Will Substituting into formula (9), we get the vertical straightness error δ z The least squares polynomial fit of (x);

[0164] Similarly, the function expressions of the relative displacement instructions corresponding to the X-axis vertical error, X-axis horizontal straightness error, Y-axis horizontal straightness error, Y-axis vertical straightness error, X-axis pitch angle error, X-axis yaw angle error, Y-axis yaw angle error and Y-axis pitch angle error can be obtained.

[0165] Furthermore, according to the functional relationship between the geometric error and the displacement command, the actual position information is corrected to obtain the compensated standard position information, and the closed-loop geometric error compensation is completed, which specifically includes:

[0166] Obtaining the structural information of the servo control system of the air floating platform, and determining the position loop information, speed loop information and current loop information, and obtaining the position command information output by the servo control system;

[0167] Based on the position loop information, a feedforward compensation link is introduced, and the functional relationship between the geometric error and the displacement command is used to correct the x in the position command information. c ,y c Make corrections to obtain the compensated position command Assume that the position command output by the servo control system at the kth sampling moment is (x c (k), y c (k)), and substituting it into the geometric error model of formula (3), we can get:

[0168]

[0169] Among them, the position instruction (x c (k),y c (k)) corresponds to three translation errors and three rotation errors.

[0170] Furthermore, according to the functional relationship between the geometric error and the displacement command, the actual position information is corrected to obtain the compensated standard position information, and the closed-loop geometric error compensation is completed, which specifically includes:

[0171] According to formula (4), the position compensation of the worktable target point P in the fixed coordinate system B is:

[0172]

[0173] The compensation in formula (13) includes the translation error and the angular error, as well as the coupling effect between the two. The compensation is added to the position command output by the servo control system to obtain the corrected command:

[0174]

[0175] Based on the speed loop information and the current loop information, the corrected instructions are input into the speed loop and the current loop, so that the servo control system drives the air floating platform to move, obtains the compensated standard position information, and completes the closed-loop geometric error compensation.

[0176] The corrected position command enters the speed loop and current loop to drive the air-floating platform to move. Since the compensation command already contains geometric error information, when the platform executes the command, the actual motion trajectory will be closer to the ideal straight line, thus achieving real-time error compensation.

[0177] It should be pointed out that since the angle error coupling term contains the coordinates of the target point P The above compensation method requires the target point position to be clear. For single-point positioning control, the target point can be selected as the feature point of the workpiece. For contour tracking control, it is necessary to select several feature points on the trajectory generated by interpolation, perform error compensation separately, and then reconstruct the compensated trajectory through fitting.

[0178] Specifically, the geometric error will cause the actual motion trajectory of the platform to deviate from the ideal straight line and reduce the positioning accuracy. To this end, this paper proposes a real-time compensation method based on error feedback. The basic idea of ​​this scheme is: first, the geometric error data of the air-floating platform during movement is obtained through laser interferometry, and then the least squares method is used to identify the error parameters to obtain the functional relationship between the geometric error and the displacement command; in real-time motion control, the identified error function is introduced into the feedforward compensation link to correct the servo reference position, thereby realizing closed-loop geometric error compensation.

[0179] It can be understood that the servo control system of the air-floating platform in this scheme adopts a three-closed-loop PID control structure. The position loop generates a speed command based on the position error, the speed loop generates a current command based on the speed error, and the current loop controls the motor output torque. If there is a geometric error in the platform, the actual displacement will deviate from the command displacement, causing a tracking error. In order to eliminate the influence of the geometric error, this scheme introduces a feedforward compensation link in the position loop.

[0180] It should be pointed out that this scheme focuses on the geometric error compensation problem of the air-floating platform. In fact, in addition to geometric errors, the air-floating platform also inevitably has deformation errors, vibration errors, thermal errors, etc. The modeling, measurement and compensation of these errors need further in-depth research. In addition, this scheme can further integrate multi-sensor information to realize real-time error measurement of the air-floating platform and introduce self-learning and adaptive strategies in compensation control.

[0181] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. A high-precision air-floating linear motion platform error analysis, measurement, and compensation method, characterized in that: include: S100, obtaining gantry structure information of the air floating platform, and constructing a fixed coordinate system B, a moving coordinate system X, a moving coordinate system Y and a moving coordinate system T based on the gantry structure information; S200, constructing a homogeneous transformation matrix through the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, and obtaining the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T; S300, obtaining a complete geometric error model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B according to the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T; S400, setting a target point, and obtaining actual position information of the target point according to a complete model of geometric errors; S500, based on the gantry structure information of the air-floating platform, build a high-precision measurement system, and obtain the geometric error data of the air-floating platform during its movement through the high-precision measurement system; S600, performing parameter identification on the geometric error data based on the least square method to obtain a functional relationship between the geometric error and the displacement instruction; S700, according to the functional relationship between the geometric error and the displacement command, the actual position information is corrected to obtain the compensated standard position information, and the closed-loop geometric error compensation is completed.

2. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 1 is characterized in that: The step of obtaining the gantry structure information of the air floating platform and constructing the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T based on the gantry structure information specifically includes: Based on the gantry structure information of the air floating platform, the marble base structure information, the X-axis drive module structure information, the Y-axis drive module structure information and the workbench structure information are obtained; According to the X-axis driving module structure information, the X-axis hydrostatic guide rail structure information and the X-axis motor driving slider structure information are obtained; According to the Y-axis driving module structure information, the Y-axis hydrostatic guide structure information and the Y-axis motor driving slider structure information are obtained; Based on the structure information of the marble base, a fixed coordinate system B is established, wherein the X axis and the Y axis of the fixed coordinate system are parallel to the length direction and the width direction of the marble base respectively; Based on the structural information of the slider driven by the X-axis motor, a moving coordinate system X is constructed, and based on the structural information of the slider driven by the Y-axis motor, a moving coordinate system Y is constructed, wherein the moving coordinate system X and the moving coordinate system Y move along the X-axis and the Y-axis of the fixed coordinate system B respectively; Based on the workbench structure information, a moving coordinate system T is constructed, and the origin of the coordinate system T is located at the intersection of the moving coordinate system X and the moving coordinate system Y.

3. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 2 is characterized in that: The homogeneous transformation matrix is ​​constructed by the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, and the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T are obtained, specifically including: Based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the worktable is controlled to move along the X-axis and Y-axis directions of the fixed coordinate system B, and the motion information of the moving coordinate system X and the moving coordinate system Y is obtained; When the workbench moves along the X-axis and Y-axis directions of the fixed coordinate system B, the position information and posture change information of the origin coordinates of the moving coordinate system T relative to the fixed coordinate system B are obtained; According to the motion information of the moving coordinate system X and the moving coordinate system Y, as well as the position information and attitude change information of the origin coordinate of the moving coordinate system T relative to the fixed coordinate system B, the homogeneous transformation matrix of formula (1) can be obtained: in, is the rotation transformation matrix of the origin coordinates of the moving coordinate system T relative to the fixed coordinate system B, is the position vector of the origin of the moving coordinate system T in the fixed coordinate system B, δ x ,δ y ,δ z are straightness errors, which represent the displacement deviations of the origin coordinates of the moving coordinate system T in the X, Y and Z directions respectively. α, β and γ are all angular errors, which represent the rotational deviations of the origin coordinates of the moving coordinate system T around the X, Y and Z axes respectively.

4. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 3 is characterized in that: The complete geometric error model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B is obtained according to the straightness error, displacement deviation and angular deviation corresponding to the moving coordinate system T, specifically including: Since the magnitude of the translation error and the rotation error is very small, R B T Do Taylor expansion near the zero point and take the first-order approximation, then we have: The p B T and R B T Substituting them into equation (1) respectively and ignoring small quantities above the second order, we can get: Formula (3) is the complete geometric error model of the air-floating platform moving in the X-axis and Y-axis directions of the fixed coordinate system B.

5. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 4 is characterized in that: The setting of the target point and obtaining the actual position information of the target point according to the complete geometric error model specifically includes: Assume that a target point on the workbench is P, then the position vector of P in the moving coordinate system T is Then the actual position of P in the fixed coordinate system B is: Formula (4) shows that the actual position of the target point P in B is not only affected by the position error of the origin T (δ x ,δ y ,δ z ), and is also affected by the coupling of the angular errors (α, β, γ).

6. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 5 is characterized in that: The high-precision measurement system is built based on the gantry structure information of the air-floating platform, and the geometric error data of the air-floating platform during movement is obtained through the high-precision measurement system, which specifically includes: Based on the gantry structure information of the air floating platform, the marble base structure information, the X-axis drive module structure information, the Y-axis drive module structure information and the workbench structure information are obtained; Based on the structure information of the marble base, determine the installation position information of the corner cube prism; Determine the laser head installation position information based on the X-direction drive module structure information and the Y-direction drive module structure information; Based on the workbench structure information, determine the interferometer installation position information; According to the installation position information of the corner cube prism, the installation position information of the laser head and the installation position information of the interferometer, the corner cube prism, the laser head and the interferometer are installed to build a high-precision measurement system; The laser of the laser head is adjusted so that the incident laser light is collinear with the X-axis of the fixed coordinate system B; based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the workbench is controlled to make a fixed distance incremental movement Δx along the X-axis movement direction of the fixed coordinate system B, and the corresponding fringe count change ΔN is recorded at the same time; According to the fixed distance incremental movement Δx and the fringe count change ΔN, the straightness error at the kth displacement point is obtained: In formula (5), λ is the laser wavelength, and the straightness error δ at all displacement points is z (x k ) is used for least squares fitting, and the continuous function expression of the X-axis vertical error δ can be obtained. z (x); Similarly, the X-axis horizontal straightness error δ can be obtained y (x), Y axis horizontal straightness error δ x (y) and Y axis vertical straightness error δ z (y); Combining the X-axis vertical error, X-axis horizontal straightness error, Y-axis horizontal straightness error and Y-axis vertical straightness error, the four straightness errors are orthogonal to each other to form the translation error vector of the air floating platform.

7. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 6 is characterized in that: The high-precision measurement system is built based on the gantry structure information of the air-floating platform, and the geometric error data of the air-floating platform during movement is obtained through the high-precision measurement system, which specifically includes: Based on the interferometer installation position information, an angle interferometer is installed, and based on the workbench structure information and the corner cube installation position information, a corner cube is installed on the workbench; Adjust the angle interferometer so that its measuring light is parallel to the X-axis of the fixed coordinate system B and the reference light is perpendicular to the X-axis; Based on the fixed coordinate system B, the moving coordinate system X, the moving coordinate system Y and the moving coordinate system T, the workbench is controlled to make a fixed distance incremental movement Δx again, and the corresponding angle fringe change ΔN is recorded. α , then the pitch angle error at the kth displacement point is: Where d is the effective aperture of the corner cube prism, for discrete data points α(x k ) performs least square fitting to obtain the continuous function α(x); Similarly, the X-axis yaw angle error β(x), the Y-axis yaw angle error γ(y), and the Y-axis pitch angle error β(y) can be measured; Combining the X-axis pitch angle error, the X-axis yaw angle error, the Y-axis yaw angle error and the Y-axis pitch angle error, the angular error vector of the air floating platform is formed; The translation error vector and rotation error vector of the air-floating platform are integrated to obtain the geometric error data during the movement of the air-floating platform.

8. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 7 is characterized in that: The method of performing parameter identification on the geometric error data based on the least square method to obtain a functional relationship between the geometric error and the displacement instruction specifically includes: Through the high-precision measurement system, the four translation error components and four rotation error components of the air-floating platform in the X and Y directions were measured one by one. The continuous function expressions of the relative displacement of the eight geometric errors were obtained by least squares fitting. Through equations (1) and (3), the geometric error of the air-floating platform is determined as a function of the displacement command; The function expression of geometric error relative displacement is obtained from discrete data using the least squares method: Get the vertical linear error δ in the X-axis direction z (x), the vertical straight line error δ z (x) is converted to an n-order polynomial: Where a0,…,a n As the parameters to be identified, the m groups of data points (x i ,δ zi Substituting )(i=1,2,…,m) into equation (9), we get the error equation: Where v i is the residual of the ith data point, let x = [x1, x2, …, x m ] T , δ z =[δ z1 ,δ z2 ,…,δ zm ] T ,a=[a0,a1,…,a n ] T , convert formula (8) into matrix form: v=Xa-δ z (9) Where X is the coefficient matrix: Based on the least squares criterion, let the error sum of squares v T When v takes a minimum value, the estimated value of a is: Will Substituting into formula (9), we get the vertical straightness error δ z The least squares polynomial fit of (x); Similarly, the function expressions of the relative displacement instructions corresponding to the X-axis vertical error, X-axis horizontal straightness error, Y-axis horizontal straightness error, Y-axis vertical straightness error, X-axis pitch angle error, X-axis yaw angle error, Y-axis yaw angle error and Y-axis pitch angle error can be obtained.

9. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 8 is characterized in that: The actual position information is corrected according to the functional relationship between the geometric error and the displacement command to obtain the compensated standard position information and complete the closed-loop geometric error compensation, which specifically includes: Obtaining the structural information of the servo control system of the air floating platform, and determining the position loop information, speed loop information and current loop information, and obtaining the position command information output by the servo control system; Based on the position loop information, a feedforward compensation link is introduced, and the functional relationship between the geometric error and the displacement command is used to correct the x in the position command information. c ,y c Make corrections to obtain the compensated position command Assume that the position command output by the servo control system at the kth sampling moment is (x c (k), y c (k)), and substituting it into the geometric error model of formula (3), we can get: Among them, the position instruction (x c (k),y c (k)) corresponds to three translation errors and three rotation errors.

10. The method for error analysis, measurement and compensation of a high-precision air-floating linear motion platform according to claim 9, characterized in that: The actual position information is corrected according to the functional relationship between the geometric error and the displacement command to obtain the compensated standard position information and complete the closed-loop geometric error compensation, which specifically includes: According to formula (4), the position compensation of the worktable target point P in the fixed coordinate system B is: The compensation in formula (13) includes the translation error and the angular error, as well as the coupling effect between the two. The compensation is added to the position command output by the servo control system to obtain the corrected command: Based on the speed loop information and the current loop information, the corrected command is input into the speed loop and the current loop, so that the servo control system drives the air floating platform to move and obtains the compensated standard position information.

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